Low-Frequency 3D Wave Propagation Modeling of the 12 May 2008

Mw 7.9 Wenchuan Earthquake

by M. Chavez,* E. Cabrera, R. Madariaga, H. Chen, N. Perea, D. Emerson, A. Salazar,M. Ashworth, Ch. Moulinec, X. Li, M. Wu, and G. Zhao

Abstract The seismic potential of southern China is associated with the collisionbetween the Indian and the Eurasian plates. This is manifested in the western SichuanPlateau by several seismically active systems of faults, such as the LongmenShan. The seismicity observed on the Longmen Shan fault includes recent eventswith magnitudes of up to 6.5, and the one of 12 May 2008 Mw 7.9 Wenchuan earth-quake. Herewith, as part of an ongoing research program, a recently optimized three-dimensional (3D) seismic wave propagation parallel finite-difference code was used toobtain low-frequency (≤0:3 Hz) 3D synthetic seismograms for the Wenchuanearthquake. The code was run on KanBalam (Universidad Nacional Autónoma deMéxico, Mexico) and HECToR (UK National Supercomputing Service) supercompu-ters. The modeling included the U.S. Geological Survey 40 × 315 km2 kinematicdescription of the earthquake’s rupture, embedded in a 2400 × 1600 × 300 km3 phys-ical domain, spatially discretized at 1 km in the three directions and a temporal dis-cretization of 0.03 s. The compression and shear wave velocities and densities of thegeologic structure used were obtained from recently published geophysical studiesperformed in the Sichuan region. The synthetic seismograms favorably compare withthe observed ones for several station sites of the Seismological and AccelerographicNetworks of China, such as MZQ, GYA, and TIY, located at about 90, 500, and1200 km, respectively, from the epicenter of the Wenchuan event. Moreover, the com-parisons of synthetic displacements with differential radar interferometry (DinSAR)ground deformation imagery, as well as of maximum velocity synthetic patterns withMercalli modified intensity isoseist of the 2008 Wenchuan earthquake, are acceptable.3D visualizations of the propagation of the event were also obtained; they show thesource rupture directivity effects of the Mw 7.9 Wenchuan event. Our results partiallyexplain the extensive damage observed on the infrastructure and towns located in theneighborhood of the Wenchuan earthquake rupture zone.

Introduction

The seismicity of central–southern China is related to thecollision between the Indian and the Eurasian plates. In thewestern Sichuan Plateau (eastern Tibetan Plateau), this colli-sion generates several seismically active systems of faults,such as the Longmen Shan fault system (Densmore et al.,2007; Robert et al., 2009), where the hypocenter of the 12May 2008Mw 7.9 Wenchuan earthquake is located at a depthof 10–20 km (U.S. Geological Survey [USGS] data, see Dataand Resources section). Among other manifestations of thecollision, recent Global Positioning System measurementsof crustal motion in the central eastern Tibetan Plateau

and its adjacent foreland indicate a shortening of about3 mm=year within the Longmen Shan region; this suggestsan average recurrence interval of seismic activity from 2000to 10,000 years (Burchfield et al., 2008). This Longmen Shanregion is located between thewestern Sichuan Plateau and theSichuan basin (Fig. 1). The Sichuan basin is part of theYangtze craton, and the collision between the latter and theTibetan Plateau is supposed to have produced the thickeningof the lower crust and the uplift of thewestern Sichuan Plateau(Wang et al., 2007). Another manifestation of this collision isthe seismicity in the region: it includes earthquakes with mag-nitudes ≤6:5 on and close to the Longmen Shan fault systemand with magnitudes up to 8 in its vicinity, at least since 1879,until the 12 May 2008 Mw 7.9 (Ms 8) event, as shown in

*Also at the Laboratoire de Géologie CNRS-ENS, Département desGéosciences, ENS, Paris, France.

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Bulletin of the Seismological Society of America, Vol. 100, No. 5B, pp. 2561–2573, November 2010, doi: 10.1785/0120090240

Figure 1 andTable 1.Notice in Figure 1 that the rupture area ofthe 2008Wenchuan event was∼40 × 315 km2, and its largestkinematic slips of∼6 to 9m (Ji and Hayes, 2008), representedby three inner rectangles of its rupture area, are locatedbetween the two concentrations of events with magnitudes≤6:5 that occurred from 1960 to 2007 and are identifiedby open circles inside the shaded ellipsoids in Figure 1.

In this work, a recently optimized 3D seismic wave pro-pagation parallel finite-difference (3DOPFD) code (Cabreraet al., 2007; Chavez et al., 2008), based on the staggeredfinite-difference method proposed by Madariaga (1976) for

the simulation of the dynamic propagation of a circular fault,was used to obtain low-frequency (≤0:3 Hz) 3D velocitysynthetics of the 12May 2008Mw 7.9Wenchuan earthquake.The supercomputers KanBalam and HECToR (see Data andResources section) were used to run the code. This paper isdivided into the following sections: a description of themathematical-computational model used, a discussion of thegeotectonic characteristics of the Longmen Shan fault systemregion, a presentation of examples of recordings obtained forthe Wenchuan Mw 7.9 event, the presentation of the resultsobtained from its modeling, and, finally, themain conclusionsof the work.

Mathematical and Computational 3DFinite-Difference Model

Since Madariaga’s (1976) study of the radiation charac-teristics of a circular fault, further developments of the stag-gered grid finite-difference method have been proposed forthe modeling of the wave propagation problem in 2D and3D media. Examples include the 2D, SH and P � SV wavepropagation in heterogeneous media (Virieux, 1984, 1986);a 2D fourth-order finite-difference approach to generateP � SV seismograms (Levander, 1988); the 2D propagationof SH waves using an irregular mesh (Moczo, 1989); the3D elastic wave propagation problem (Olsen, 1994); the 3Dseismic wave propagation in an elastic medium (Graves,1996); and the use of nonuniform grid spacing on the 3D elas-tic seismic wave propagation problem (Pitarka, 1999). Themethod has also been successfully applied for the modelingof thewave propagation of recent seismic events; for example,the 1992Ms 7.3 Landers, California, earthquake (Olsen et al.,1997), the 28 September 2004 Mw 6.0 Parkfield, California,earthquake (Liu et al., 2006; Custodio et al., 2009), as well asfor an Ms 7.75 earthquake scenario in the San Andreas fault(Olsen et al., 1995) and the 1906 San Francisco, California,earthquake (Aagaard et al., 2008a, 2008b).

Herewith, first a synthesis of the elastodynamic formu-lation (based on Minkoff, 2002) and a description of the 3Doptimized parallel algorithm (Cabrera et al., 2007; Chavezet al., 2008) of the elastic wave propagation problem arepresented.

Elastodynamic Formulation of the Elastic WavePropagation Problem

For the velocity-stress formulation of the elastic waveequation in a 3Dmediumoccupying a volumeV and boundaryS, the mediummay be described using Lamé parameters λ� �x�and μ� �x� and mass density ρ� �x�, where � �x�∈R3 (Minkoff,2002). The velocity-stress form of the elastic wave equationconsists of nine coupled, first-order partial differentialequations for the three particle velocity vector componentsνij� �x; t� and the six independent stress tensor components,σij� �x; t�, where i, j � 1, 2, 3, and assuming thatσij� �x; t� � σji� �x; t�:

Figure 1. Fault systems in the region of interest are identifiedby bold lines with a number (modified from Wang et al., 2007): 1,Longmen Shan; 2, Xianshuihe; 3, Anninghe; 4, Garze–Litang; 5,Jinshajiang; 6, Xiangcheng; 7, Longriba. Rivers are indicated bythin lines: a, Jinshajiang; b, Yellow. Open circles denote the epicen-ters of earthquakes with magnitudes >5 that occurred from 1960 to2007. The epicenters of M ≥ 7:2 historical earthquakes are identi-fied with the letters A–D and with W for the 12 May 2008 Wench-uan event (see Table 1). AA′ and BB′ correspond to the seismicprofiles studied by Wang et al., (2007); CC′, DD′, and EE′ identifythe seismic profiles studied by Xu et al., (2007). The surface pro-jection of the rupture area of the 12 May 2008 Mw 7.9 Wenchuanearthquake is represented by the long rectangle, and its inner rec-tangles identify the areas with kinematic slips >6 to 9 m suggestedby Ji and Hayes (2008). The color version of this figure is availableonly in the electronic edition.

Table 1Large Magnitude (M ≥7:2) Earthquakes in/near the

Longmen Shan Fault System, 1879–2009

EventDate

(dd/mm/yyyy) MMI* MDepth of

Earthquake (km)

A 01/07/1879 XI 8.0 —B 25/08/1933 X 7.5 —C 16/08/1976 IX 7.2 15D 23/08/1976 VIII� 7.2 23W 12/05/2008 XI 8.0 10

*MMI is the maximum Mercalli modified intensity of theearthquakes. (See Fig. 1 for the epicentral location of the events.)

2562 M. Chavez et al.

∂vi� �x; t�∂t � b� �x� ∂σij� �x; t�

∂xj � b� �x��fi� �x; t� �

∂maij� �x; t�∂xj

�;

(1)

and

∂σij� �x; t�∂t � λ� �x� ∂vk� �x; t�∂xk δij � μ� �x�

�∂vi� �x; t�∂xj � ∂vj� �x; t�

∂xi�

� ∂msij� �x; t�∂t ; (2)

where b� �x� � 1=ρ� �x�, fi� �x; t� is the force source tensor,ma

ij� �x; t� � 1=2�mij� �x; t� �mji� �x; t�� and msij� �x; t� � 1=2

�mij� �x; t� �mji� �x; t�� are the antisymmetric and symmetricsource moment tensors, and δij is the Kronecker delta func-tion. The traction boundary condition (normal component ofstress) must satisfy

σij� �x; t�nj� �x� � ti� �x; t� (3)

for �x on S, where ti� �x; t� are the components of the time-varying surface traction vector and nj� �x� are the componentsof the outward unit normal to S. The initial conditions onthe dependent variables are specified at V and on S at timet � t0 by

vi� �x; t� � v0i � �x�; σij� �x; t� � σ0ij� �x�: (4)

If the orientation of interest is on a particular axis definedby the dimensionless unit vector e, then the particle velocityseismogram is given by

ve� �xr; t� � ekvk� �xr; t�� e1v1� �xr; t� � e2v2� �xr; t� � e3v3� �xr; t�: (5)

In our simulations, the sourcewas assumed to have zero resul-tant force and moment so that fi� �x; t� � 0 andma

ij� �x; t� � 0.The symmetric moment tensor density is defined as m �μ� �x�D� �x�, where D is the slip. For a general fault shape,we project the moment density into the closest points onthe grid (Olsen et al., 1997).

Parallel Implementation of the 3D Optimized ParallelFinite-Difference Code

The finite-difference staggered algorithm applied toequations 1–4 is an explicit scheme that is second-order ac-curate in time and fourth-order accurate in space. Staggeredgrid storage allows the partial derivatives to be approximatedby centered finite differences without doubling the spatialextent of the operators, thus providing more accuracy. Thediscretization of the 3D spatial grid is such that xi � x0��i � 1�hx, yj � y0 � �j � 1�hy, and zk � z0 � �k � 1�hz fori � 1; 2; 3;…I, j � 1; 2; 3;…; J, and k � 1; 2; 3;…; K,respectively. Here x0, y0, z0 are the minimum grid values,and hx, hy, hz indicate the distance between points in thethree coordinate directions. The time discretization is defined

by tl � t0 � �l � 1�ht for l � 1; 2; 3;…; L. Here, t0 is theminimum time and ht is the time increment. Further detailsabout the (velocity-stress) staggered finite-difference schemeon which the algorithm used is based can be found inMadariaga (1976), Olsen (1994), Graves (1996), and Moczoet al. (2005).

The best parallel programs are those where each proces-sor gets almost the same amount of work while trying tominimize communications. Using this kind of partition, theglobal domain is decomposed into smaller pieces (subdo-mains) and distributed among all processors; therefore, eachprocessor solves its own subdomain problem.

We use message passing interface (MPI) to parallelizethe 3DOPFD code. In particular, MPI_Bcast was used tocommunicate the geometry and physical properties of theproblem before starting the wave propagation loop, andMPI_Cart_Shift and MPI_SendRecv were used to update thevelocity and stress calculations at each time step. The fourth-order spatial finite-difference scheme requires two additionalplanes of memory on every face of the subdomain to computethe finite-difference solution independently from the otherprocesses; therefore, we allocate padded subdomains ofmem-ory for every face of the subdomain cube to ensure the precisefunctioning of the staggered finite-difference scheme used.

Other details about the implementation, tests, and bench-mark studies performed on different supercomputer platformsof the developed 3DOPFD optimized code can be found inCabrera et al. (2007) and Chavez et al. (2008).

Geotectonic Characteristics of the Region around theLongmen Shan Fault System

With respect to the structural geotectonic characteristicsof the region of interest (Fig. 1), Li et al. (2006) recently pro-posed 14 crustal models for mainland China. Those modelswere the result of∼90 seismic refraction/wide angle reflectionprofiles and included representative crustal seismic velocity(in particular of compression waves, VP)–depth columns,associated to the 14 tectonic units of China proposed byT. K. Huang et al. in 1980 (quoted by Li et al. 2006). In thiswork, the geotectonic characteristics of the depth columnsF,H, and L, of figure 5 fromLi et al. (2006)were used becausethey include the region depicted in Figure 1, as well as othernortheastern regions that were included in the modeled phy-sical domain of the Mw 7.9 Wenchuan earthquake (Fig. 2).

At a regional level, Wang et al. (2007) performed activesource seismic refraction and wide-angle reflection (i.e.,deep seismic sounding) experiments in the western SichuanPlateau and the Sichuan basin region. From those experi-ments, Wang et al. (2007) obtained 2D seismic profiles ofthe transects AA′ (which include the Longmen Shan faultsystem) and BB′ shown in Fig. 1. The lengths of both tran-sects were of ∼700 km, and the resolution depths were up to80 km. A reference altitude of 3 km (i.e., reflecting thevarying topography of the region) was used for processingthe information (Wang et al., 2007). Based on those seismic

Low-Frequency 3D Wave Propagation Modeling of the 12 May 2008 Mw 7.9 Wenchuan Earthquake 2563

profiles, they proposed the 3D geotectonic structure of about700 × 700 × 80 km3 shown in Figure 3, as well as the cor-responding compression velocity (VP) and density values ofthe crust layers up to the mentioned 80 km depth (Wang et al.,2007). Notice in Figure 3 that the Wang et al. (2007) crustlayering proposal for the Longmen Shan region consists of(almost) horizontal layers for the 700 × 700 km2 studiedregion.

The variation of the shear wave velocity, VS, with depthfor the same Sichuan region studied by Wang et al. (2007)(i.e., the seismic profiles CC′, DD′, and EE′ of Fig. 1) was

obtained by Xu et al. (2007). They applied the receiver func-tion technique to very broadband (VBB) recordings of tele-seismic earthquakes in 25 temporal stations, disseminated inthe Sichuan region at altitudes from 0 (on the Sichuan basin)to 4 km (on the western Sichuan Plateau); see Figure 1.Among other results, they obtained the VS crustal velocitiesup to a depth of 80 km for profiles that included some stationsites located in the vicinity of the Longmen Shan fault sys-tem. Of particular interest for this work is the result shown infigure 10 of Xu et al. (2007): in the first 7 km of depth; theVS values are significantly inferior to 3 km=s. Xu et al.(2007) also proposed ratios of VP=VS for the mentionedstation sites, which, on average are equal to 1:86� 0:07.

It is important to mention that the results obtained byWang et al. (2007) and Xu et al. (2007) show a smooth 2Dvariation of the VP, VS, and density values found for theregion included in Figure 1 and Figure 3. Those values re-flect the properties of the layers forming the topography ofthe Sichuan region shown in these two figures; for example,the recording station sites MC03 (∼15 km of the LongmenShan fault system) and MC04 of figure 10 of Xu et al.(2007), located at altitudes of 2 and 4 km, respectively.

Observations of the 12 May 2008 Mw 7.9Wenchuan Earthquake

A large number of seismographs and accelerographs ofthe Seismological Network of China (SNC) and of the ChinaDigital Strong Motion Network (CDSMN) recorded the 12May 2008Wenchuan event. However, the accelerographic in-formation recorded for this event by the 478 instruments of theCDSMN (Yuan and Sun, 2008) is not available to the public forthe time being (except, in this work, the ones recorded at thestation MZQ; see Fig. 2 and the Data and Resource section)and from the 48 VBB digital seismographs of the SNC, theinformation from 17 of which was available for this study(see Data and Resource section). Unfortunately, most of theseismograms were saturated for the mainshock of the 2008Wenchuan event.

Figure 2. The surficial projection of the 2400 × 1600×300 km3 volume used to discretize the region of interest. Smallrectangle, the 315 × ∼40 km2 southwest–northeast-directed rupturearea of the 12 May 2008 Wenchuan Mw 7.9 earthquake; star, loca-tions of its epicenter; dots, the CD2, GYA, and TIY seis-mographic stations sites; MZQ, the accelerographic station site ofthe China Seismographic and Accelerographic Networks (modifiedfrom Ji and Hayes, 2008). The color version of this figure is avail-able only in the electronic edition.

Figure 3. 3D diagram of the crustal kinematic model for the eastern margin of the Tibetan Plateau, constructed from 2D crustal structuresobtained from the seismic profiles AA′ and BB′ of Figure 1 (modified from Wang et al., 2007).

2564 M. Chavez et al.

In Figures 4–6, we present examples of the velocity VBBseismograms recorded for the Ms 8 Wenchuan earthquake atCD2, GYA, and TIY stations (see Fig. 2), located at about90 km (near field), 500 km (intermediate field) and 1200 km(far field) from its epicenter, respectively. Notice in thosefigures that the seismograms at CD2 station are saturated from∼190 to 550 s (Fig. 4); however, the ones for GYA areunsaturated, from ∼190 to 290 s and saturated from ∼290to ∼450 s (Fig. 5), and the TIY records are unsaturated from∼260 to 380 s and saturated from ∼380 to 500 s (Fig. 6)—thatis, the maximum amplitudes of the ground motion velocitiesat those stations could not be recorded because the VBBseismographs of the SNC reached their maximum range.Therefore, for the present study, for which the main objectiveis the generation of low-frequency synthetic seismograms forthe 12 May 2008 Wenchuan event, we decided to use theselected unsaturated time windows of the velocity recordingsof stations GYA and TIY shown in Figure 5 and Figure 6,respectively, as well as to low pass filter them for frequencies≤0:3 Hz in order to compare them with the syntheticsseismograms.

Because the recordings of stations GYA and TIY wereobtained at epicentral distances of ∼500 km and ∼1200 kmand because we were also interested in using near-fieldrecordings for the study, this information was provided bythe accelerograms recorded at station MZQ, located at about90 km from the epicenter of the Mw 7.9 Wenchuan earth-quake, (Fig. 2). In the top panel of Figure 7, we show thevertical component of those recordings. Notice that, in thiscase, the record is not saturated and reached a maximumacceleration of 6:23 m=s2 and that the duration of its mostintense part was ∼25 s. The record was integrated once toobtain the associated velocity signal (middle panel of Fig. 7),and then a time window of 100 s was selected and low-passfiltered for frequencies≤0:3 Hz (bottom panel of Fig. 7). ThisMZQ velocity seismogram and the previously mentionedseismograms from GYA and TIY stations were comparedwith the synthetic seismograms obtained with the 3DOPFDcode for the 12 May 2008 Wenchuan Mw 7.9 earthquake.

3D Modeling of the Wave Propagation of the 12May 2008 Wenchuan Mw 7.9 Earthquake

Geologic and Geophysical Parametersof the Modeling

The 3DOPFD code was used for the computation of low-frequency synthetic seismograms for the Mw 7.9 Wenchuanearthquake. The information required by the code about thegeometric and mechanical properties (VP, VS, and densities)of the physical domain of interest, the seismic source (strike,dip, rake, and slip) and the spatial and temporal discretizationparameters are discussed below.

With respect to the selected physical domain, thesurface projection of the 2400�length� × 1600�width�×300�depth� km3 volume used in this work is presented inFigure 2. Notice in this figure that the surface includes theprojection of the 315 × 40 km2 Wenchuan Mw 7.9 earth-quake rupture area (Ji and Hayes, 2008), as well as the loca-tions of the recording stations MZQ, CD2, GYA, and TIY.The 300-km depth of the volume took into account thepossible generation of long-period surface waves in the in-termediate (GYA station) and far (TIY) fields of the consid-ered assumed domain. The geologic structure assumed forthis volume is depicted in Figure 8. Notice that this structureincludes seven layers with a total thickness of 48 km restingon a last one of 252 km and that the first layer (starting from

Figure 4. Very broadband velocity (saturated from ∼190 to∼550 s) seismograms in the East (E), North (N), and vertical (Z)directions observed at station CD2 (see Fig. 2) of the SeismologicalNetwork of China for the 12 May 2008 Mw 7.9 Wenchuanearthquake.

Figure 5. Very broadband velocity (saturated from ∼290 to∼550 s) seismograms in the North (N) direction observed at stationGYA (see Fig. 2) for the 12 May 2008 Mw 7.9 Wenchuan earth-quake and the 100-s (unsaturated, from ∼190 to ∼290 s) selectedtime window filtered for frequencies ≤0:3 Hz.

Figure 6. Very broadband velocity (saturated from ∼380 to∼500 s) seismograms in the North (N) direction observed at stationTIY (see Fig. 2) for the 12 May 2008Mw 7.9 Wenchuan earthquakeand the 62-s (unsaturated) selected time window filtered forfrequencies ≤0:3 Hz.

Low-Frequency 3D Wave Propagation Modeling of the 12 May 2008 Mw 7.9 Wenchuan Earthquake 2565

the top) has a shear wave velocity of propagation consider-ably smaller than the other layers.

It is relevant to mention that the geologic structureshown in Figure 8, and its corresponding thicknesses, VP,VS, and densities, were adopted here as a first approach(which should be improved in a future study when more geo-logic information becomes available) to the modeling of thegeologic structure for the region of interest depicted inFigure 2. The geologic structure of Figure 8 took the regionalstructural geotectonic and geophysical information availablefor the Sichuan region into account; that is, in the firstinstance, the selection considered the geometry and layeringof the crust of the kinematic volume (about 700 × 700×80 km3) proposed by Wang et al. (2007) and shown inFigure 3 for the region surrounding and including the seismicsource of the Mw 7.9 Wenchuan earthquake (Robert et al.,2009). Based on seismologic and gravity data, Robert et al.(2009) concluded that the hypocenter of the 12 May 2008Wenchuan earthquake is located very close to a westward-dipping interface (starting close to the surface at the Long-men Shan front and flattening at ∼15 km depth) betweenthe lower crust under the Sichuan basin and the easternSongspan-Garze terrane (see fig. 2 of Robert et al., 2009).

With respect to the thicknesses, the VP, VS, and densitiesof the layers included in Figure 8 (and particularly the mostsurficial ones), we took into account the findings about thoseproperties obtained by Wang et al. (2007), Xu et al. (2007),and Li et al. (2006), which were discussed previously. TheVP, VS, and densities of the layers suggested by Wang et al.(2007) and Xu et al. (2007) were obtained for the seismicprofiles AA′, BB′ and CC′, DD′, EE′ of Figure 1 for referencealtitudes from 0 to 4 km and up to a depth of 80 km, taking intoaccount the layering and the mechanical properties of thehigh and low altitudes of the Sichuan region and its vicinity.Therefore, we think that, even thoughwe are not including thetopography of the Sichuan region in our flat layering modelshown in Figure 8, the synthetic seismograms of theWenchuanMs 8 earthquake computed here with the geologic

structure of Figure 8 for sites at epicentral distances in the nearfield (e.g., the MZQ station site) and intermediate field (GYArecording station site) would better reflect the geologicconditions of the Sichuan region than those for the far field(e.g., the TIY recording station site) sites located at largeepicentral distances and with different geologic conditionsthan the ones of the Sichuan region, particularly for theirsurficial layers, as discussed by Li et al. (2006).

Seismic Source and Discretization Parametersof the Modeling

In this work, the kinematic slip distribution shown inFigure 9, obtained by Ji and Hayes (2008), as well as thestrike, dip, and rake angles of the event listed by the USGS(see Data and Resources section) for the Mw 7.9 Wenchuanearthquake were adopted for the modeling. The slip distribu-tion proposed by Ji and Hayes (2008) was obtained from theinversion of teleseismic wave forms and using a discretization

Figure 7. Recorded accelerogram and its velocity seismogramin the vertical (Z) direction observed at station MZQ (see Fig. 2) forthe 12 May 2008 Mw 7.9 Wenchuan earthquake and the 100-sselected time window filtered for frequencies ≤0:3 Hz.

Figure 8. The geologic structure adopted in this work for thevolume used to discretize the region of interest (see Fig. 2). Thestructure was obtained from averaging the China-regional resultsof Li et al. (2006) and the local results (see Fig. 1 and Fig. 3) forthe Sichuan region of Wang et al. (2007) and Xu et al. (2007). Thecolor version of this figure is available only in the electronic edition.

2566 M. Chavez et al.

of the seismic source area of 315 × ∼ 40 km, with21 × 8 cells of 15 × 5 km2 in the strike and dip directionsof the event, respectively. As shown in Figure 9, they obtainedmaximum slips of∼9 min two regions of the rupture area, oneat ∼50 km and the second at ∼180 km from the hypocenter.This slip distribution was converted into a moment ratedistribution and used as the seismic source in the finite-difference code.

The earthquake rupture had a strike of 229°, a dip of 33°,and a rake of 141°, with a southwest–northeast rupture direc-tion and total rupture duration of ∼120 s. A uniform rupturevelocity of 2:75 km=s was assumed for the seismic source.The slip rate function was a box-car with a rise time of 1 sand a total duration of 2.5 s. The seismic moment M0 1:15×1021 Nm and thrust mechanism were assumed for the event(Ji and Hayes, 2008).

The discretization parameters used in this study are pre-sented in Table 2. The spatial discretization in the threedirections was 1 km, and the time discretization was 0.03 s.The number of grid points were 2400, 1600, and 300 for theX, Y, and Z directions (see Fig. 2), and a total of 20,000 timesteps were used for a total simulation time of 600 s. Table 2includes the minimum VP and VS velocities, as well as theminimum density of the layers of the geologic structure ofFigure 8. Notice that the spatial and temporal discretizationsused, as well as the VPmax

of 8 km=s of the geologic structure(Fig. 8), comply with the Courant–Friedrichs–Lewy (CFL)condition (i.e., a CFL of 0.24) to guarantee the stability andconvergence of the solution (i.e., the synthetic velocity seis-mograms of the discretized media).

Modeling Results

General Observations. With the geologic, geophysical,seismic source, and discretization parameters discussed pre-viously in this paper, the computation with the 3DOPFD codeof the low-frequency synthetics for the 12 May 2008Mw 7.9

Wenchuan earthquake was carried out on the supercomputersKanBalam and HECToR (see Data and Resources section).

The 3DOPFD code previously has been successfullyused to obtain near-field and far-field low-frequency syn-thetics of the 19 September 1985 Ms 8.1 Michoacan,Mexico, earthquake (Cabrera, et al., 2007; Chavez et al.,2008). For those studies, the authors used the slip distributionsuggested by Mendoza and Hartzell (1989), who, for thesource inversion of the 1985 Michoacan event, used near-field and teleseismic waveform data low-pass filtered at0.5 Hz and utilized 120 subfaults of 15 × 13:9 km2, eachof them to obtain the slip distribution of the event. Mendozaand Hartzell (1989) pointed out that the slip distribution theyobtained could only model source frequencies ≤0:5 Hz.

One of the numerical experiments performed by Cab-rera, et al. (2007) for the 1985 Michoacan event consistedof using spatial discretizations in the three directions of 1.0,0.5, and 0.25 km of a 500 × 600 × 125 km3 physical domainand temporal discretizations of 0.03, 0.02, and 0.01 s, respec-tively, in order to comply with the CFL condition. An impor-tant result of those studies was that, even though theoreticallythe computed synthetic seismograms (Cabrera, et al., 2007;Chavez et al., 2008) for the 0.5 and 0.25-km spatial discre-tization should have a frequency content larger than 1 Hz, theFourier amplitude spectra of the corresponding syntheticshad very small values at a frequency of ∼0:3 Hz (<0:5 Hz)for all the previously mentioned space and temporal discre-tizations. This result is in agreement with Mendoza and Hart-zell (1989), who emphasized the 0.5-Hz limit of their sourceinversion.

Taking these results into account, as well as the fact thatthe slip distributions of Ji and Hayes (2008) for the Mw 7.9Wenchuan event were obtained with the inversion of teleseis-mic data and 168 subfaults of 15 × 5 km2 each, to model theevent 315 × 40 km2 rupture area; therefore, the maximumfrequency modeled for the Ji and Hayes (2008) source inver-sion is 0.5 Hz (Chen Ji, personal comm., 2010), as in theMendoza and Hartzell (1989) inversion of the 1985 Michoa-can earthquake. For these reasons, we decided to restrict ourstudy to synthetics with frequencies up to 0.3 Hz.

The main objective of this work was the 3D modeling ofthe low-frequency (≤0:3 Hz) wave propagation generated by

Figure 9. Kinematic slip and the strike, dip, and rake of the 12May 2008 WenchuanMw 7.9 earthquake proposed by Ji and Hayes(2008). Dashed line rectangles indicate the regions with slips from∼6 to ∼9 m (modified from the USGS Web site, see Data andResources section). The color version of this figure is available onlyin the electronic edition.

Table 2Parameters for the 3D Low-Frequency Modeling

Parameter Value

Spatial discretization (km) 1.0Temporal discretization (s) 0.03P-wave minimum velocity (km=s) 4.5S-wave minimum velocity (km=s) 2.4Minimum density (Ton=m3) 2.5Number of grid points, X direction 2400Number of grid points, Y direction 1600Number of grid points, vertical direction 300Number of time steps 20000Simulation time (s) 600

Low-Frequency 3D Wave Propagation Modeling of the 12 May 2008 Mw 7.9 Wenchuan Earthquake 2567

the 12 May 2008 Wenchuan earthquake and then to comparethe modeling results with different types of observations ofthe wave propagation and the effects of this event, particu-larly in the vicinity of the rupture zone of this earthquake, asfollows: (1) to compare the synthetic seismograms with theones observed at the near (MZQ accelerographic station site),intermediate (GYAVBB seismographic station site), and far(TIY VBB seismographic station site) field recordings; (2) toobtain 3D visualizations of the low-frequency syntheticvelocity wave field for the region of interest, and particularlyfor the one surrounding the Longmen Shan fault system,where the effects of the wave propagation of the earthquakewere the most important; (3) to compare the syntheticsresults with surface differential radar interferometry (Din-SAR) ground deformation imagery available for specificzones of the Sichuan region; and (4) to compare the regional3D synthetic velocities wave-field results with the Mercallimodified intensities observed mainly on and in the vicinityof the rupture zone of the 2008 Wenchuan event.

Comparison of Synthetic Seismograms with SeismogramsObserved at the Near-Field, Intermediate-Field, and FarField Recordings. For the comparisons of synthetics withthe observations in Figures 10 and 11, we present examplesof the type of results obtained from the modeling. Figure 10includes the time domain comparisons for the three stationsites, and the frequency domain comparisons are presentedin Figure 11. In Figure 10a, the observed and syntheticvelocity seismograms in the vertical (Z) direction for the nearfield stationMZQ, located at an epicentral distance of∼90 km(Fig. 2) are shown. As mentioned previously in this paper,the observed velocity seismogram corresponds to a unsatu-rated recorded accelerogram with a total duration of ∼160 s(Fig. 7), recorded practically on top of the seismic source ofthe Wenchuan 2008 event, from which a 100-s window wasselected.

The window of the observed seismogram includes thefirst arrivals, as well as the surface and the coda waves, pro-pagating from the source to the MZQ site. As the triggeringtime of the accelerograph of the MZQ station was not avail-able, the S-wave arrival time on both seismograms was cho-sen as the criteria for selecting the starting time for thesynthetic. Notice in Figure 10a that the overall shape and themaximum amplitudes of both the observed and the syntheticseismograms are similar, particularly for the first arrivals andthe surface wave (i.e., up to 50 s); however, from 50 to 60 s,the synthetic amplitudes are larger than the observed ones,and the opposite occurs from 60 to 100 s.

With respect to the phase comparisons of the observedand synthetic signals, we observe some phase differences onthe surface and coda waves of the synthetic with respect tothe observed record. The comparison of the observed and thesynthetic seismograms in the frequency domain is shown inFigure 11a. From this figure it can be concluded that, as awhole, the shapes of the spectra are similar, although theFourier amplitudes of the synthetic are about half of the

observed for f ≤ 0:04 Hz, up to twice as high from 0.06to 0.1 Hz, up to four times (at 0.15 Hz) higher between0.1 and 0.2 Hz, and the same from 0.2 to 0.25 Hz.

We think that the results obtained for the MZQ syn-thetics from the 3D modeling are reasonable, taking into con-sideration that: (1) the actual local soil conditions at thestation site are unknown and that they have been onlyapproximately incorporated by the geologic structure adopt-ed in this work, particularly by the VS velocities of the first4-km layer (from the top) shown in Figure 8; (2) the topog-raphy effects on the station site seismic response have notbeen included in the flat layering (Fig. 8) modeling usedherewith; and (3) the assumptions made about a uniform rup-ture velocity of the seismic source of a complex geologyregion such as the Longmen Shan fault system and theSichuan region as a whole, as Robert et al. (2009) and Dens-more et al. (2007) have pointed out.

The comparison of the time and frequency domains forthe observed and synthetic seismograms for the intermediatefield (500-km epicentral distance), VBB seismographic GYAstation is shown in Figure 10b and Figure 11b, respectively.As noted previously, the observed seismogram correspondsto a 100-s window of the unsaturated part of the 1800-srecord (see Fig. 5); therefore, the modeling for this station

Figure 10. Observed and synthetic velocity seismograms(≤0:3 Hz) for the 12 May 2008 Wenchuan Mw 7.9 earthquake:(a) in the vertical (Z) direction for station MZQ, epicentral distance90 km (see Fig. 2); (b) in the north (N) direction for station GYA,epicentral distance of 500 km (see Fig. 2); (c) in the north (N) direc-tion for station TIY, epicentral distance of 1200 km (see Fig. 2). Thecolor version of this figure is available only in the electronic edition.

2568 M. Chavez et al.

aims to generate the synthetics corresponding to the firstarrivals. From the comparison in the time domain shown inFigure 10b, it can be concluded that the overall shapes ofboth the observed and the synthetic seismograms are similar;however, from 0 to 70 s, the maximum amplitudes of thesynthetic are about 60% of the observed ones, and between70 and 100 s, the amplitudes are very similar. There are somedifferences in the phases of the synthetic with respect to theobserved one. With respect to the frequency domain compar-ison, from Figure 11b, we observe that their shapes are verysimilar and that, from 0.01 to 0.10 Hz, the Fourier amplitudesof the observed seismograms are higher (up to 60%) than thecorresponding amplitudes of the synthetics; however, from0.1 to 0.2 Hz, the synthetic Fourier amplitudes are higherthan the corresponding observed ones.

From the time and frequency domain comparisons of theGYA seismograms, we can conclude that the results are, as awhole, acceptable for the same reasons that were mentionedearlier with respect to the MZQ synthetic. However, we think

that for station GYA the adopted geologic structure ofFigure 8, specially of the most surficial layers, the effectsof not knowing the actual superficial layering and its proper-ties becomes critical; therefore, the differences between thetime and frequency domain characteristics of the syntheticand the observed seismograms have to be larger thanfor MZQ.

The comparison of the time and frequency domains forthe observed and synthetic seismograms for the far (1200-kmepicentral distance) field, VBB seismographic TIY stationis shown in Figure 10c and Figure 11c, respectively. Theobserved seismogram correspond to a 60-s window of theunsaturated part of a 1800-s record (see Fig. 6); therefore,the modeling objective for this station consists of the genera-tion of the synthetic corresponding to the first arrivals. Fromthe comparison in the time domain shown in Figure 10c, weobserve that, even though the amplitudes are similar, the phasedifferences of the two signals are large. With respect to thefrequency domain comparison from Figure 11c, we observethat their shape is very similar and that the Fourier amplitudesof the observed and synthetic seismograms are close from0.01 to 0.5 Hz. From those comparisons, we can conclude thatthe modeling results for TIY station are acceptable, better inthe frequency domain than in the time domain. We think thatthe reasons for these are basically the same as that alreadymentioned for station GYA.

3D Visualizations of the Low-Frequency Synthetic VelocitiesWave Field for the Region of Interest. With respect to the3D low-frequency synthetic velocities wave field for the re-gion of interest, in Figures 12–14, 3D snapshots at t � 24:24,72.24, and 100.56 s of the synthetic velocities wave fields(≤0:3 Hz) in the Y direction, obtained for the 12 May 2008Mw 7.9 Wenchuan earthquake modeling are shown, respec-tively. The visualizations were obtained for a reduced domainof 900 × 800 × 70 km3 because the amplitudes of the veloci-ties wave field were too small to be visualized for the original2400 × 1600 × 300 km3 of Figure 2. Notice that the maxi-mum and minimum velocities are in the Mw 7.9 Wenchuanearthquake rupture direction (X direction, parallel to thestrike of the event) and perpendicular to it (Y direction),respectively. This observation from the synthetic wave propa-gation pattern obtained here corresponds to the importantinfrastructure destruction observed for towns such asYingxiu,Dujiangyang, and Beichuan, as well as to the very slightdamage observed at Chengdu (see Figs. 12–14 for the towns’locations) and reported by Yuan and Sun, 2008. From otherresults not shown here, the following conclusions can bemen-tioned: (1) the largest amplitudes in the X, Y and Z syntheticvelocity wavefields occurred in the positive X direction,which correspond to the rupture direction of the Wenchuanearthquake reported by the USGS Web site (see Data andResources section); (2) the smaller amplitudes in the X andY wavefields occurred in a cone-shaped volume generatedby a 30° angle (for the X wavefield) to 60° angle (for theY wavefield), approximately in the Y direction.

Figure 11. Fourier amplitude spectra for the seismograms ofFigure 10. The color version of this figure is available only inthe electronic edition.

Low-Frequency 3D Wave Propagation Modeling of the 12 May 2008 Mw 7.9 Wenchuan Earthquake 2569

Comparison of Synthetics Results with Surface DinSARGround Deformation Imagery. For comparison of the syn-thetics results with DinSAR images available for specificzones of the Sichuan region for theMw 7.9 Wenchuan earth-quake (Figure 15 and Figure 16), we show the low-frequencysynthetic displacement seismograms obtained for the townsof Chengdu and Beichuan. Notice in Figure 15 that a max-imum displacement, Dmax, of ∼0:12 m was obtained atChengdu for the X and Y directions and of ∼0:07 m for theZ direction and that permanent displacements of ∼ � 0:04 mfor the Y direction and of ∼ � 0:03 for the Z direction wereobtained in the modeling. The corresponding results forBeichuan are the following: Dmax values of �0:71, �3:31,and �2:87 m for the X, Y, and Z, directions, respectively;

maximum permanent displacements are ∼� 0:4, ∼ � 1:5,and ∼� 0:45 m in the X, Y, and Z directions, respectively.

The comparison of synthetic displacements obtained forBeichuan and Chengdu with DinSAR ground deformationimagery (Fig. 17) is as follows. The DinSAR ground defor-mations results reported for the Beichuan region are of �5 mto �5 m, and specially of �1 m to �1 m, which are of theorder of the maximum permanent synthetic displacementsconsigned for Beichuan. Finally, from the same figure it canbe observed that the DinSAR ground deformations resultreported for the vicinity of the Chengdu region is of 0.12 m,which is also of the order of the maximum permanent syn-thetic displacements values of the synthetics for this town.From these results, we think that the comparisons of the syn-thetic displacements obtained in this work are in reasonableagreement with the DinSAR results of Ge et al. (2008) andStramondo et al. (2008) for the 2008 Wenchuan earthquake,taking into account what we already mentioned previously inthis paper with respect to the comparisons of the synthetics

Figure 12. 3D Snapshot (reduced for visualization purposes to900 × 800 × 70 km3 of the modeled volume; see Fig. 2) at t �24:24 s of the synthetic velocities wave field (≤0:3 Hz) in the Ydirection for the 12 May 2008 Wenchuan Mw 7.9 earthquake.The darker and thicker wave field identifies the southwest–northeastrupture direction of the Wenchuan event. Points 1 to 7 correspond tothe locations of Yingxiu, Zipingku, Dujiangyang, Chengdu,Beichuan, Jiangyou, and Mianyang, respectively. The color versionof this figure is available only in the electronic edition.

Figure 13. 3D snapshot (reduced for visualization purposes to900 × 800 × 70 km3 of the modeled volume; see Fig. 2) at t �72:24 s of the synthetic velocities wave field (≤0:3 Hz) in the Ydirection for the 12 May 2008 Wenchuan Mw 7.9 earthquake.The darker and thicker wave field identifies the southwest–northeastrupture direction of the Wenchuan event. Points 1 to 7 correspondto the locations of Yingxiu, Zipingku, Dujiangyang, Chengdu,Beichuan, Jiangyou, and Mianyang, respectively. The color versionof this figure is available only in the electronic edition.

Figure 14. 3D snapshot (reduced for visualization purposes to900 × 800 × 70 km3 of the modeled volume; see Fig. 2) at t �100:56 s of the synthetic velocities wave field (≤0:3 Hz) in theY direction for the 12 May 2008 Wenchuan Mw 7.9 earthquake.The darker and thicker wave field identifies the southwest–northeastrupture direction of the Wenchuan event. Points 1 to 7 correspond tothe locations of Yingxiu, Zipingku, Dujiangyang, Chengdu,Beichuan, Jiangyou, and Mianyang, respectively. The color versionof this figure is available only in the electronic edition.

Figure 15. Displacement synthetics of the 12 May 2008Wenchuan Mw 7.9 earthquake obtained for seismographic stationsite CD2 (Chengdu; see Fig. 17).

2570 M. Chavez et al.

with the observed seismograms for the recording stationssites of MZQ, GYA, and TIY.

Comparison of Regional 3D Synthetic Velocities Wave-FieldResults with Mercalli Modified Intensities Observed on andnear the Rupture Zone. With respect to the comparison ofthe regional 3D synthetic maximum velocities wave-fieldresults with the Mercalli modified intensities (MMI) observedmainly on and in the vicinity of the rupture zone of the 2008Wenchuan event, the comparison of the maximum syntheticvelocity patterns in the Y direction with the MMI isoseistof the 2008 Wenchuan earthquake (reported in fig. 3.1 inYuan and Sun, 2008) is presented in Figure 18. Notice, in

this figure, that the maximum synthetic velocities globallycorrespond with the zones where the reported intensitieswere X and XI, as for example in Beichuan; the same obser-vation applies to the minimum synthetic velocities with thezone of intensities VI, such as in Chengdu; however, there isa discrepancy for the epicentral region, where a regional MMIof XI was observed versus an MMI of IX associated with themaximum synthetic velocity. (See the right side of the figurefor the relationship between the ground velocity and MMI.)Nevertheless, from these results, we think that the compar-isons of the regional 3D synthetic maximum velocities wave-field results with the MMI (observed mainly on and in thevicinity of the rupture zone) of the 2008 Wenchuan eventare as whole reasonable, if we take into account what wealready mentioned with respect to the comparisons of thesynthetic with the observed seismograms for the recordingstation site of MZQ.

Conclusions

A recently optimized 3D seismic wave propagation par-allel finite-difference code was used to obtain low-frequency(≤0:3 Hz) 3D synthetic seismograms for the 12 May 2008Mw 7.9 Wenchuan earthquake. The synthetics were obtainedon the surface projection of a volume of 2400 × 1600×300 km3; the volume included the 40 × 315 km2 kinematicdescription of the earthquake rupture. The spatial and tem-poral modeling discretizations were 1-km and 0.03 s, respec-tively. The comparison between the observed and synthetic

Figure 16. Displacement synthetics of the 12 May 2008Wenchuan Mw 7.9 earthquake obtained for Beichuan (see Fig. 17).

Figure 17. Maximum ground displacements near Chengdu and Beichuan using DinSAR ground deformation imagery (A, Stramondoet al., 2008; B, Ge et al., 2008) for the 12 May 2008 Mw 7.9 Wenchuan earthquake. The color version of this figure is available only in theelectronic edition.

Low-Frequency 3D Wave Propagation Modeling of the 12 May 2008 Mw 7.9 Wenchuan Earthquake 2571

seismograms for several station sites of the Seismologicaland Accelerographic Networks of China (MZQ, GYA,and TIY) located at about 90, 500, and 1200 km from theepicenter of the Wenchuan event, respectively, is acceptable.The comparisons of the maximum permanent synthetic dis-placements with DinSAR ground deformation imagery, aswell as of maximum velocity synthetic patterns with Mercallimodified intensity isoseists of the 2008 Wenchuan earth-quake are also acceptable. From the 3D visualizations of thepropagation of the modeled earthquake obtained in thiswork, the largest amplitudes in the X (rupture direction),Y (perpendicular to X), and Z velocity wave fields occurredin the rupture direction of the Wenchuan earthquake. Theseresults partially explain the extensive damage observed onthe infrastructure and towns located on top and in the neigh-borhood of the Wenchuan earthquake rupture zone.

Data and Resources

The supercomputers KanBalam (Universidad NacionalAutónoma de México, Mexico) and HECToR (UK NationalSupercomputing Service) were used to run the code. Theseismograms used in this study were provided by the Seis-mological Network of China and the accelerogram from sta-tion MZQ by the China Digital Strong Motion Network, andthey cannot be released to the public. The kinematic slip dis-tribution, the strike, dip, and rake of the 2008 Wenchuanearthquake were obtained from the U.S. Geological SurveyPreliminary Result of the May 12, 2008, Mw 7.9 Eastern

Sichuan, China, Earthquake, Finite Fault Model usinghttp://earthquake.usgs.gov/earthquakes/eqinthenews/2008/us2008ryan/ (last accessed May 2008).

Acknowledgments

We would like to thank J. L. Gordillo, G. Lucet, and the supercomput-ing staff of the Dirección General de Cómputo Acádemico (DGSCA),UNAM, as well as M. Ambriz and the computing staff of the Institute ofEngineering, UNAM, for their support. Also, we would like to thank E. Cha-vez for helping us to obtain the seismological information of the Wenchuanearthquake in May–June 2008. We acknowledge DGSCA, UNAM for thesupport to use KanBalam, and the facilities of HECToR, the UK’s nationalhigh-performance computing service, which is provided by UoE HPCx Ltdat the University of Edinburgh, Cray Inc., and NAG Ltd, and funded by theOffice of Science and Technology through the Engineering and PhysicalSciences Research Council’s High End Computing Programme. The authorsalso acknowledge support from the Scientific Computing Advanced Train-ing (SCAT) project through Europe Aid contract II-0537-FC-FA (http://www.scat‑alfa.eu). Thoughtful reviews from anonymous reviewers signifi-cantly improved the manuscript.

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Institute of EngineeringUniversidad Nacional Autónoma de MéxicoCiudad Universitaria, 04510Mexico DF, Mexico

(M.Ch., N.P.)

Dirección General de Servicios de Cómputo AcadémicoUniversidad Nacional Autónoma de MéxicoCiudad Universitaria, 04510, Mexico DF, Mexico

(E.C., A.S.)

Laboratoire de GéologieCentre National de la Recherche ScientifiqueEcole Normale SuperieureDépartement des Géosciences24 Rue Lhomond, Paris, France

(R.M.)

China Earthquake Network Center63 Fuxing Rd.Beijing 100036, People’s Republic of China

(H.C., M.W., G.Z.)

STFC Daresbury LaboratoryDaresbury Science & Innovation CampusWarrington WA4 4AD, UK

(D.E., M.A., C.M.)

Institute of Engineering Mechanics, Chinese Academy of SciencesChina Earthquake Administration29 Xuefu Rd.Harbin 150080, People’s Republic of China

(X.L.)

Manuscript received 31 August 2009

Low-Frequency 3D Wave Propagation Modeling of the 12 May 2008 Mw 7.9 Wenchuan Earthquake 2573